Find f'(x) for y = (x+5 / x+1) (2x+1)

I don't know how to proceed here. Do I use the quotient rule inside the first brackets? Then what?

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- Dec 6th 2009, 08:33 AMArchduke01Derivatives involving both product/quotient rule
Find f'(x) for y = (x+5 / x+1) (2x+1)

I don't know how to proceed here. Do I use the quotient rule inside the first brackets? Then what? - Dec 6th 2009, 08:43 AMlvleph
First thing you can do is use the product rule

$\displaystyle y' = \frac{d}{dx}\left[\frac{x+5}{x+1}\right] \cdot (2x+1) + 2\cdot

\frac{x+5}{x+1}$.

From here we can take the derivative using the quotient rule on $\displaystyle \frac{d}{dx}\left[\frac{x+5}{x+1}\right] = \frac{(x+1) - (x + 5)}{(x+1)^2}$.

Combine this with the previous result

$\displaystyle y' = \frac{(x+1) - (x + 5)}{(x+1)^2} \cdot (2x+1) + 2\cdot

\frac{x+5}{x+1}$.

Now simplify. - Dec 6th 2009, 08:51 AMArchduke01
- Dec 6th 2009, 09:10 AMlvleph
Yes, that is what www.wolframalpha.com gives.